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Simplifying (x2 + 3y) * dy + -1(x + -1y) * dx = 0 Reorder the terms for easier multiplication: dy(x2 + 3y) + -1(x + -1y) * dx = 0 (x2 * dy + 3y * dy) + -1(x + -1y) * dx = 0 (dx2y + 3dy2) + -1(x + -1y) * dx = 0 Reorder the terms for easier multiplication: dx2y + 3dy2 + -1dx(x + -1y) = 0 dx2y + 3dy2 + (x * -1dx + -1y * -1dx) = 0 Reorder the terms: dx2y + 3dy2 + (1dxy + -1dx2) = 0 dx2y + 3dy2 + (1dxy + -1dx2) = 0 Reorder the terms: 1dxy + -1dx2 + dx2y + 3dy2 = 0 Solving 1dxy + -1dx2 + dx2y + 3dy2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'd'. d(xy + -1x2 + x2y + 3y2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(xy + -1x2 + x2y + 3y2)' equal to zero and attempt to solve: Simplifying xy + -1x2 + x2y + 3y2 = 0 Solving xy + -1x2 + x2y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + -1x2 + x2y + -1xy + 3y2 = 0 + -1xy Reorder the terms: xy + -1xy + -1x2 + x2y + 3y2 = 0 + -1xy Combine like terms: xy + -1xy = 0 0 + -1x2 + x2y + 3y2 = 0 + -1xy -1x2 + x2y + 3y2 = 0 + -1xy Remove the zero: -1x2 + x2y + 3y2 = -1xy Add 'x2' to each side of the equation. -1x2 + x2y + x2 + 3y2 = -1xy + x2 Reorder the terms: -1x2 + x2 + x2y + 3y2 = -1xy + x2 Combine like terms: -1x2 + x2 = 0 0 + x2y + 3y2 = -1xy + x2 x2y + 3y2 = -1xy + x2 Add '-1x2y' to each side of the equation. x2y + -1x2y + 3y2 = -1xy + x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + 3y2 = -1xy + x2 + -1x2y 3y2 = -1xy + x2 + -1x2y Add '-3y2' to each side of the equation. 3y2 + -3y2 = -1xy + x2 + -1x2y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -1xy + x2 + -1x2y + -3y2 Simplifying 0 = -1xy + x2 + -1x2y + -3y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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